DGM for the Solution of Nonlinear Dynamic Elasticity

  • Miloslav FeistauerEmail author
  • Martin Hadrava
  • Jaromír Horáček
  • Adam Kosík
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)


The subject of the paper is the numerical solution of dynamic elasticity problems. We consider linear model and nonlinear Neo-Hookean model. First the continuous dynamic elasticity problem is formulated and then we pay attention to the derivation of the discrete problem. The space discretization is carried out by the discontinuous Galerkin method (DGM). It is combined with the backward difference formula (BDF) for the time discretization. Further, several numerical experiments are presented showing the behaviour of the developed numerical method in dependence on the coefficient in the penalty form. At the end the developed method is applied to the simulation of vibrations of 2D model of human vocal fold formed by four layers with different materials.



This research was supported under the grants of the Czech Science Foundation No. 17-01747S (M. Feistauer, M. Hadrava, A. Kosík) and 16-01246S (J. Horáček).


  1. 1.
    J. Česenek, M. Feistauer, A. Kosík, DGFEM for the analysis of airfoil vibrations induced by compressible flow. Z. Angew. Math. Mech. 93(60–67), 387–402 (2013)MathSciNetCrossRefGoogle Scholar
  2. 2.
    P.G. Ciarlet, The Finite Element Method for Elliptic Problems. Studies in Mathematics and Its Applications, vol. 4 (North-Holland, Amsterdam, 1978)Google Scholar
  3. 3.
    P.G. Ciarlet, Mathematical Elasticity, Volume I, Three-Dimensional Elasticity. Studies in Mathematics and its Applications, vol. 20 (Elsevier Science Publishers B.V., Amsterdam, 1988)Google Scholar
  4. 4.
    V. Dolejší, M. Feistauer, Discontinuous Galerkin Method, Analysis and Applications to Compressible Flow. Springer Series in Computational Mathematics, vol. 48 (Springer, Cham, 2015)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Miloslav Feistauer
    • 1
    Email author
  • Martin Hadrava
    • 1
  • Jaromír Horáček
    • 2
  • Adam Kosík
    • 1
  1. 1.Charles UniversityFaculty of Mathematics and PhysicsPraha 8Czech Republic
  2. 2.Institute of Thermomechanics, The Academy of Sciences of the Czech RepublicPraha 8Czech Republic

Personalised recommendations